Analyzing locality over a P2P computing architecture

Abstract

A characteristic of Peer-to-Peer (P2P) computing networks is their huge number of different computational resources scattered across the Internet. Gathering peers into markets according to their multi-attribute computational resources makes it easier to manage these environments. This solution is known as market overlay. In this context, the closeness of the markets with similar resources, known as locality, is a key feature for ensuring good P2P resource management. Thus, the locality feature over a market overlay allows a lack of resources in a given market to be compensated quickly by any other market with similar resources, whenever these are close to each other. Consequently, locality becomes an essential challenge.

This paper addresses the analysis of the locality of P2P market over-lays. According to this, a new procedure for measuring locality is applied together with an extensive analysis of some well-known structured P2P overlays. Based on this analysis, a new P2P computing architecture, named DisCoP, oriented towards optimizing locality is proposed. Our proposal gathers the peers into markets according to their computational resources. A Hilbert function is used to arrange multi-attribute markets in an ordered and mono-dimensional space and the markets are linked by means of a Bruijn graph. In order to maintain the DisCoP locality whenever the overlay is not completed, a solution based on the virtualization of markets is also proposed. Finally, the DisCoP locality is tested together with the proposed virtualization method for approximate searches over uncompleted overlays. The simulation results show that approximate searches exploit the DisCoP locality efficiently.

Introduction

Peer-to-Peer (P2P) computing is a distributed computing paradigm that uses large numbers of autonomous hosts as a platform for executing applications. Properties such as decentralization, self-organization, dynamism and fault-tolerance make these systems naturally scalable and attractive solutions for applications in all areas of distributed computing (Foster and Iamnitchi, 2003). The efficient scheduling and executing of these applications over a P2P computing platform needs a mechanism to search and manage the set of peers whose available computational resources (i.e. CPU, Memory or Bandwidth) fit the requirements of the application to be executed. Taking both the large-scale and mutable amount of computational resources provided by each peer into account, resource management in P2P computation becomes a research challenge (Lua et al., 2005).

In order to manage the huge number of different computational resources scattered across the network, some studies Gupta et al. (2006) and Meshkova et al. (2008) propose to group peers with similar computational attributes into markets. Thus, the search time for the requested computational resources is significantly reduced and unnecessary outgoing queries are minimized. Unfortunately, the lookup queries are totally unbalanced, as those markets made up of peers with the most popular computational resources are those the users require most. Thus, the peers of the most popular markets rapidly become busy and, as a consequence, the system receives an avalanche of unsuccessful queries. P2P computing platforms should accordingly provide alternative resources with capabilities as close as possible to those requested, a term known as approximate searches. So locality, thought of in terms of market proximity, is a key aspect when designing structured networks for P2P computing systems. We are interested on the locality or clustering defined in il Jeong et al. (2008) as a value that indicates the closeness of the markets with similar computational resources (called similar markets henceforth) mapped into a multi-dimensional space using the distances provided by a specific overlay.

To this end, our paper analyzes the benefits of providing proximity or locality to a P2P computing environment. In order to do so, a new procedure is also provided to measure the degree of locality of any topology. The application of the proposed procedure for any given P2P overlay returns one absolute metric to analyze the real magnitude of the locality and other relative metric to make easier the comparison between different overlays. Based on this, we analyze the locality features of some well-known P2P topologies, such as Chord (Stoica et al., 2001) or Bruijn (Loguinov et al., 2003), together with the Hilbert Space-Filling Curve (SFC) (Xu and Tirthapura, 2012). Note that Hilbert SFC is often used in P2P structured topologies to transform k-dimensional coordinates into 1-D space (Shen et al., 2008). Our locality results reveal that the combination of Hilbert and Bruijn obtains a locality gain of up to 80% compared with other overlays.

Taking the locality features of the analyzed topologies into account, a new architecture named DisCoP (Distributed Computing Platform), orientated towards P2P computing, is described. The DisCoP architecture is made up of a Hilbert mapping function plus a two-layer overlay. The Hilbert function allows peers to be classified into markets according to their computational attributes. These markets are linked by means of the DisCoP two-layer overlay. The top layer interconnects the markets by means of a Bruijn graph, while the nodes in the same market are arranged into a tree topology in the bottom layer. In addition, the linkage of similar markets over the DisCoP overlay are optimized by means of adding extra-links, which allow the intrinsic locality provided by the Hilbert SFC in the Bruijn topology to be maintained. Our simulation results reveal that the interaction between the three levels of the DisCoP architecture (Hilbert, Bruijn and Tree levels) together with the added extra-links allows the best degree of market locality to be achieved. It means that our proposal locates similar computing resource providers (markets) as close as possible to each other.

Unfortunately, whenever the Bruijn graph is not complete, the locality falls drastically. In order to solve this, a solution based on the virtualization of markets (Kaashoek and Karger, 2003) is proposed. Finally, the DisCoP locality is applied, together with the proposed virtualization method, to locate approximate resources whenever the requested resources do not exist because the Bruijn graph is incomplete. Thus, a method is provided for carrying out approximate searches over the DisCoP platform. Our experimentation shows that our approximate search method is able to exploit DisCoP locality efficiently.

The outline of this paper is as follows. The related work is described in Section 2. A P2P computing system model is described in Section 3. The metrics and a procedure for obtaining the locality of a P2P computing overlay are proposed in Section 4. Section 5 introduces the proposed DisCoP architecture. The analysis of the DisCoP locality is carried out in 6 Analysis of the DisCoP locality, 7 Virtualization of markets explains the virtualization method proposed to maintain locality over an uncompleted Bruijn graph. An example of the application of the locality and virtualization to find approximate queries is given in Section 8. Finally, the main conclusions and future work are explained in Section 9.